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The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system's wavefunction at that position.
Quantum mechanics is intrinsically indeterministic. The correspondence principle: in the appropriate limit, quantum theory comes to resemble classical physics and reproduces the classical predictions. The Born rule: the wave function of a system yields probabilities for the outcomes of measurements upon that system.
The old quantum theory is a collection of results from the years 1900–1925 [23] which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. [24] The theory is now understood as a semi-classical approximation [25] to modern quantum mechanics. [26]
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from the usual mathematical representation of measurements in quantum physics together with the assumption of non-contextuality.
The definition of quantum theorists' terms, such as wave function and matrix mechanics, progressed through many stages.For instance, Erwin Schrödinger originally viewed the electron's wave function as its charge density smeared across space, but Max Born reinterpreted the absolute square value of the wave function as the electron's probability density distributed across space; [3]: 24–33 ...
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The Born rule states that an observable property of a quantum system is defined by a Hermitian operator on a separable Hilbert space, that the only observable values of the property are the eigenvalues of the operator, and that the probability of the system being observed in a particular eigenvalue is the square of the absolute value of the ...